you have different forces for different masses. The acceleration depends on the masses of both objects, therefore the acceleration is different for a heavier ball and a lighter ball. Of course, if we're talking about two object easily held in the hand versus the Earth, then the difference would be negligible to the point of almost being nonexistent. But, technically, they would fall at "different" rates.

So much this. Congratulations on being one of the few non-crackpots in this thread.

Nope. The two objects would accelerate at exactly the same rate (at first).

For object 1, the accerlation is given by:

a1 = Fg / m1 = (G * m1 * mE / r^2) / m1 = G * mE / r^2

For object 2, the acceleration is given by:

a2 = Fg / m2 = (G * m2 * mE / r^2) / m2 = G * mE / r^2

That is, the acceleration is independent of the object's mass.

The thing that will make the heavier object fall (very so slightly) faster is that the Earth is also drawn to the objects, and the Earth will move slightly faster toward the heavier object than the lighter one, thus decreasing the radius faster on the heavier object than the lighter object, meaning the heavier object starts to accelerate faster.

Wow, old news is exciting! Nordtvedt has been at this for decades. I used a lot of his work in my undergrad research project. For further reading, check out my advisor's 2000 paper: http://arxiv.org/abs/gr-qc/0007047 I worked to try to extend that paper to other solar system bodies. I made some progress, but it was a dead end and another student has picked it up and is heading in a slightly different direction.

The basic idea is that many "beyond the standard model" proposals introduce a field that couples to matter differently than gravity. Perhaps nuclear binding energy plays a role. Perhaps it's proton to neutron ratio. There are many proposed fields out there. Now, just as gravity is far weaker than electromagnetism, this proposed field is much weaker than gravity, so any effects would be very small. It is already constrained to the 1 part in 1013 by lunar laser ranging and torsion balances. That still leaves plenty of room for a new field to hide.

There have been a few satellite projects proposed to measure this effect even more sensitively. Some of the Gravity Probe B guys are working on STEP (Satellite Tests of the Equivalence Principle) which would theoretically be able to measure any deviation to one part in 1018. The Europeans are working on a project called MICROSCOPE that will work similarly. These satelliteexperiments wouldn't be terribly expensive, but unfortunately, big projects like the JWST take up all of the funding.

Smeggy Smurf:I always figured the object with the greater mass fell faster because the more massive object's additional gravity helped things along

The object with the greater mass feels a greater force, yes. However, because it's more massive, it takes more force to accelerate it at the same rate as a smaller mass. It's actually very fascinating that there are two types of mass, and as far as we can tell, they're exactly the same. Mass is the gravitational "charge." It's what determines how strong a gravitational field is. It's ALSO what causes resistance to acceleration. At first glance, these two things should have nothing to do with one another. The fact that they are equal is one of the foundations of Einstein's general relativity.

Well, of course it does. This is kinda like how Newton was mostly right unless you're traveling at relativistic speeds and what not. For objects of extremely low mass, like everything we deal with every day, the pull exerted on the Earth is so negligible that it really isn't even necessary to consider it, thus everything accelerates at about the same rate, +- 10-30 m/s or whatever the actual error would be. It's really the mass difference between the two objects that matter when disregarding the smaller mass, so the Earth or Moon compared to the Sun is like a 20 pound cannonball or a 10 pound cannonball compared to Earth.

Otherwise, the actual equation for acceleration due to gravity is F= G * ((m1 * m2) / r2), which makes it quite obvious that both masses effect acceleration. If a second Earth mass planet magically popped up nearby, the rate at which it would accelerate towards the Earth would be at least twice that of a much less massive object, like the cannonball. Well, really, this second planet would accelerate towards the earth at the usual rate we're used to, but the Earth would also accelerate towards this second planet by the same amount, thus from the reference point of the Earth (and all reference points must be valid), the second planet would be accelerating twice as fast as a much less massive object.

St_Francis_P:Kome: St_Francis_P: At least that's the idea. The Nordtvedt effect has been tested, and so far no evidence has been found that the more massive Earth is falling towards the sun faster than the moon. If there is an effect, it's very slight.

So some guy had an idea, but there's no evidence it's correct. In fact, it seems to be wrong. This is truly game changing.

That is how science works.

It is, but usually it doesn't become a featured article afterward.

Actually science journalism is almost dead in America.

Even Perez Hilton posting famous women on his shiatty blog and calling them whores is more insightful and educational these days.

NASA only releases rocks and CGI generated deep field "photographs" and the same speculations we've had since the 70's.

Quantum is so misunderstood you can just skip any article about it and save what little you might know from driving you insane.

New products using centuries old conepts with an LED attached are masquraded as "progress"

And, if you wait around, once every day some jackass asks "Whar flying car, whar?" and sells it to a newspaper as an editorial.

Kome:St_Francis_P: At least that's the idea. The Nordtvedt effect has been tested, and so far no evidence has been found that the more massive Earth is falling towards the sun faster than the moon. If there is an effect, it's very slight.

So some guy had an idea, but there's no evidence it's correct. In fact, it seems to be wrong. This is truly game changing.

At least that's the idea. The Nordtvedt effect has been tested, and so far no evidence has been found that the more massive Earth is falling towards the sun faster than the moon. If there is an effect, it's very slight.

So some guy had an idea, but there's no evidence it's correct. In fact, it seems to be wrong. This is truly game changing.